Solucion analítica y semianalítica del movimiento circular vertical con fricción
DOI:
https://doi.org/10.31349/RevMexFis.23.020211Keywords:
Nonlinear differential equation, Adomian decomposition method, Vertical circular motion, TrackerAbstract
En este trabajo, se presenta un estudio del movimiento circular vertical con fricción, modelado mediante una ecuación diferencial no lineal de primer orden. Se obtiene una solución analítica del modelo original y, adicionalmente, se aplica el Método de Descomposición de Adomian como técnica semianalítica. Los resultados se validan experimentalmente mediante análisis de video con el software Tracker, encontrando una buena concordancia entre teoría y experimento.
This paper presents a study of vertical circular motion with friction, modelled by a first-order nonlinear differential equation. It is obtained an analytical solution for the original model, and, additionally, the same problem is solved semi-analytically using the Adomian Decomposition Method. The results are experimentally compared through video analysis using Tracker software, An acceptable agreement between the experiment and the theoretical solutions is reported.
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References
R. Cross, Sliding and rolling along circular tracks in a vertical plane, American Journal of Physics 91 (2023) 351
R. C. Maldonado et al., Estudio teórico-experimental de la dinámica del movimiento circular con fricción, Rev. Mex. Fis. E 18 (2021) 020204
R. Cross, Motion of a metal nut sliding around a vertical loop, Physics Education 59 (2024) 033001
C. E. Mungan, Over the top, The Physics Teacher 59 (2021) 680
O. Bertran and J. Riba, A revised solution for a sphere rolling in a vertical loop, European Journal of Physics 42 (2020) 015008
W. Kłobus, Motion on a vertical loop with friction, American Journal of Physics 79 (2011) 913
L. P. Franklin and P. I. Kimmel, Dynamics of circular motion with friction, American Journal of Physics 48 (1980) 207
I. A. C. Melnik and V. d. A. Oliveira, Análise do movimento de uma partícula em um loop circular vertical usando noções de limite, Revista Brasileira de Ensino de Física 42 (2020) e20190244
A. Bettini, A Course in Classical Physics 1-Mechanics, Undergraduate Lecture Notes in Physics (Springer International Publishing, 2016), https://books.google.com.mx/books?id=6TTeCwAAQBAJ
J. Miljojkovic et al., Loop-the-loop as a real tribomechanical system applicable in engineering education (2021)
G. Adomian, Nonlinear stochastic operator equations (Academic press, 2014)
G. Adomian and R. Rach, On composite nonlinearities and the decomposition method, Journal of mathematical analysis and applications 113 (1986) 504
G. Adomian, Applications of nonlinear stochastic systems theory to physics (1987)
Y. Zhu, Q. Chang, and S. Wu, A new algorithm for calculating Adomian polynomials, Applied Mathematics and Computation 169 (2005) 402
R. G. G. d. Amorim et al., Resolvendo Equações Diferenciais pelo Metodo da Decomposição de Adomian, Revista Brasileira de Ensino de Física 42 (2020) e20200095
M. K. Mak, C. S. Leung, and T. Harko, A brief introduction to the Adomian decomposition method, with applications in astronomy and astrophysics, arXiv preprint arXiv:2102.10511 (2021)
O. Alomari et al., Solution for projectile motion in two dimensions with nonlinear air resistance using Laplace decomposition method, J. Math. Comput. Sci. 12 (2022) Article
M. K. Mak, C. S. Leung, and T. Harko, The effects of the dark energy on the static Schrödinger-Newton system-An Adomian Decomposition Method and Pade approximants based approach, Modern Physics Letters A 36 (2021) 2150038
A.-M. Pendrill, Student investigations of the forces in a roller coaster loop, European journal of physics 34 (2013) 1379
S. Alberghi et al., Is it more thrilling to ride at the front or the back of a roller coaster?, The Physics Teacher 45 (2007) 536
A.-M. Pendrill and D. Eager, Velocity, acceleration, jerk, snap and vibration: Forces in our bodies during a roller coaster ride, Physics Education 55 (2020) 065012
Tracker Video Analysis and Modeling Tool for Physics Education, https://opensourcephysics.github.io/tracker-website/
B. Asavapibhop and N. Suwonjandee, Loop-the-Loop: An Easy Experiment, A Challenging Explanation, In AIP Conference Proceedings 1263 (2010) 249-251
P. Bhakat, S. Chakraborty, and P. Mandal, Tracking the motion of a simple pendulum with tracker, Resonance 29 (2024) 1085
G. U. Varieschi, The projectile inside the loop, Physics Education 41 (2006) 236, https://doi.org/10.1088/0031-9120/41/3/005
P. L. Tea Jr, Trouble on the loop-the-loop, American Journal of Physics 55 (1987) 826
R. Cross, Loop the loop experiments, Physics Education 57 (2022) 065018
M. M. Khater et al., Analytical and semi-analytical solutions for time-fractional Cahn-Allen equation, Mathematical Methods in the Applied Sciences 44 (2021) 2682
M. M. Khater et al., Analytical, semi-analytical, and numerical solutions for the Cahn-Allen equation, Advances in Difference Equations 2020 (2020) 9
R. Cross, Rotating ring on a horizontal rod, Physics Education 59 (2024) 015037
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